Yesterday I bought two tickets to a movie, which logically had consecutive numbers. I examined the numbers, which had four digits, and mentioned that the sum of the eight digits was 25.

A friend asked if any digit appeared more than twice out of the eight, and I answered him.

Other friend asked if the sum of the digits of either ticket was equal to 13, which I also answered.

And then, to my surprise, my daughter told me what the two numbers were!

What were they?

Okay, let's assume that the daughter knew what the two ticket numbers were.

We have four different possibilities as to how the two questions would be answered.

They would be (question 1 and question 2 answered sequentially) yes, yes; yes, no; no, yes; no, no

Let's first take yes, yes.

The father would know that, between the two tickets, there would be one of the digits appearing more than twice and that the sum of the digits on one of the tickets would equal 13.
The only way that the daughter would get the correct numbers would be pure luck since there are a number of possibilities. Nonetheless, it is still a possibility that she could guess the correct numbers.

Next, let's take yes, no.

This means that she could deduce that the two numbers would end in 99 and 00 (for instance, the numbers 0399 and 0400 or 3099 and 3100).
Her chances here of getting the correct numbers would be a lot better, and there is a better chance she could guess the correct numbers on the tickets.

Thirdly, let's take no, yes.

Of the four combinations I think that no, yes provided the most possibilities, so her chances of guessing the correct numbers is fairly remote.
Again, nonetheless, there is that chance.

Finally, there is no, no.

This combination provides the best chance of getting the correct numbers, for there is only one possibility and that would be 1299,1300.

Of all the possibilities, this would be the answer that would MOST LIKELY be given.

But since there is even the slightest possibility that she could guess correctly on any of the other combinations, I can't safely say that 1299 and 1300 is the ONLY answer.

It is AN answer, but not THE answer.

Posted by James on 2005-11-25 15:53:23